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An application of integer programming to playoff elimination in football championships

Abstract: Football is the most followed and practiced sport in Brazil, with a major economic importance. Thousands of jobs depend directly from the activity of the football teams. The Brazilian national football championship is followed by millions of people, who attend the games in the stades, follow radio and TV transmissions, and check newspapers, radio, TV, and, more recently, the Internet in search of information about the performance and chances of their favorite teams. Teams which are not qualified to the playoffs loose a lot of money and are even forced to dismantle their structure. We comment and compare the complexity of playoff elimination in football and baseball championships. We present two integer programming models which are able to detect in advance when a team is already qualified to or eliminated from the playoffs. Results from these models can be used not only to guide teams and fans, but are also very useful to identify and correct wrong statements made by the press and team administrators. The application and the use of both models in the context of the 2002 edition of the Brazilian national football championship are discussed.

This type of application can be developed in a straightforward way in (say) java, with calls to the Orion integer programming solver via the web services. One interesting angle on this is to use applications like this as analytics tools for sports betting. For example if you could find an instance where teams were eliminated from contention, but this fact was sufficiently difficult to see from current standings (requiring knowledge of the schedule and possible outcomes thereof), you could have opportunities to place bets in zero risk situations where the other side takes the bet without benefit of your knowledge. For example I could give you 10000-1 odds against a particular soccer team winning a championship, knowing that it’s mathematically impossible for them to even make the playoffs. You might take the bet if you can’t tell that that is the case. You could even automate this by using the betfair API to automatically query for betting possibilities where you know the outcome and automatically place bets in those circumstances… and just passively let the money roll in.